PHY-105
Assignment #3
Due before 11:59pm Friday, 25 February 2011
Problem 1 [8 pts]
Lets go back to again look at the last problem from assignment #2.
Explain, being as quantitative as you can:
(a) Will the distribution predicted in part (c) be in fact the distribution that actually occurs ?
Why or why not ?
(b) Given the result from part (b) why aren’t the Paschen series lines (those to/from the n=3
state) considered in our treatment of the hydrogen lines we expect to observe for typical surface
temperatures of stars.
(c) In order to calculate N2 /Ntotal needed for estimates of the Balmer series strength, we made
the assumption that NI = N1 + N2 in order to give us ratios we could easily calculate from the
Boltzmann and Saha equations. Justify this assumption for typical surface temperatures of stars.
Problem 2 [5 pts]
In class we used the approximation that nearly all the H-I atoms are in the ground state so that
we could estimate the partition function;
Z1 ≈ g1 = 2(1)2 = 2
Verify that this statement is correct for a temperature of 10,000 K by evaluating the first three
terms in the partition function.
Problem 3 [7 pts]
Explain clearly why the calcium-II absorption lines in the Sun are about a factor of 400 stronger
than the H-I Balmer lines when there is only one calcium atom for every 500,000 hydrogen atoms
in the Sun’s surface layer.
Problem 4 [7 pts]
Text, Problem 2.7. Note for this problem the calculation is for the H − ion (a proton orbited by 2
electrons), not the H atom we looked at in class (H − ions are only important for very cool stars
so we didn’t look at this in detail – but there’s a hint for the ball-park answer you should expect
to get!). Note that singly ionized H − is simply an H atom.
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Problem 5 [6 pts]
Sirius, the brightest appearing star in the night sky, has an apparent bolometric magnitude of;
mbol = −1.55.
The distance to Sirius is 2.6 pc. Determine the absolute bolometric magnitude of Sirius and
compare it with that of the Sun. What is the ratio of Sirius’ intrinsic luminosity to that of the
Sun ?
Problem 6 [10 pts]
For parts of this problem, you’ll need to refer back to the lecture notes from the first couple of
lectures.
Consider a star assumed to be a spherical blackbody with surface temperature 15,000 K, radius
of 4.0×109 m, and located at a distance of 100 pc from Earth. Determine the following for this star:
(a) Luminosity.
(b) Absolute magnitude.
(c) Apparent magnitude.
(d) Distance modulus.
(e) Radiant flux at the star’s surface.
(f ) Radiant flux at the Earth’s surface (compare to what we calculated for the Sun).
(g) The peak wavelength, λmax .
Problem 7 [7 pts]
Assuming that 10 eV could be released by every atom in the Sun through chemical reactions,
estimate how long the Sun could shine at its current rate through chemical processes alone. For
simplicity assume that the Sun is composed entirely of hydrogen. Is it possible that the Sun’s
energy is entirely based on chemical reactions ? (You will need to look up the mass and luminosity
of the Sun and the mass of a hydrogen atom – given in class and on assignment 1.)
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